基于Zoeppritz方程的广角反射振幅和相位特征分析

发布时间：2018-04-11 12:03

  本文选题：Zoeppritz方程 + 位移函数　； 参考：《西南石油大学》2016年硕士论文

【摘要】：地震波在遇到分界面时将会产生同类反射波,转换反射波和转换透射波,以及折射和全反射等物理现象,我们称这种物理现象为地震波在分界面上的广义散射。这部分的内容是地震波场传播理论的重要组成部分,也广泛应用于油气,水合物等地震勘探开发领域。地震波在自由界面以及弹性界面的散射的研究包含两个方面：一方面是波动方程和界面边界条件的边值定解问题,而另一方面就是该边值定解问题的求解过程。一言以蔽之,我们求解地震波的分界面上的散射就是确定波动方程满足的边值定解问题,然后求出该边值定解问题的解函数的过程。然而边值定解问题又分为位移位和位移这两种表达形式,故存在两种不同的研究方式。采用位移位函数进行研究,我们称之为”位移位方法”,位移位方法的典型代表即为"Knott"方程。而采用位移函数进行研究的方法,称为“位移方法”,位移方法的典型代表即为‘'Zoeppritz"方程。位移方法以及位移位方法在物理含义上保持一致,但在数学解法上却存在着些许差异。本文主要论及平面纵波谐波人射到弹性介质分界面上产生反射纵波、反射横波、透射纵波、透射横波时给位移位振幅方程组。本文采用位移波函数进行研究,首先讲述关于Zoeppritz方程的的一些基本问题,主要包括位移形式的边值定解问题以及求解该边值定解问题的解函数。归纳推导在地震勘探坐标系下P波和SV波分别从四个象限入射的Zoeppritz方程。求解Zoeppritz方程首先设定满足定解问题波动方程的平面波函数,该波函数包含有入射波,同类型反射波,同类型透射波以及转换反射波和转换透射波五种具体波,规定这些波射线上体积元的偏振方向,接着把波函数代入界面方程,同时我们还定义反射系数以及透射系数,最后整理出来的解函数即为相对应的Zoeppritz方程。然后对Zoeppritz方程进行数值计算,通过数值计算可以使我们更加清晰更加透彻的认识地震波在不同条件的界面上散射规律。当入射角到达临界角附近时,透射波则沿分界面滑行,而当入射角大于临界角时,透射波此时退化成为不均匀波,不均匀波的波数以及反射系数均为复数,广角反射接收到的就是这段能量。我们通过合成地震记录发现,在临界角附近的振幅和相位的急剧变化,由于临界角的存在使得反射波同相轴扭曲复杂化。
[Abstract]:The seismic waves will produce the same kind of reflection wave, converted reflection wave and converted transmission wave, as well as refraction and total reflection. We call this kind of physical phenomenon the generalized scattering of seismic wave on the boundary surface.This part is an important part of seismic wave field propagation theory and is widely used in seismic exploration and development fields such as oil and gas hydrate and so on.The study of seismic wave scattering at free interface and elastic interface includes two aspects: on the one hand, the boundary value solution problem of wave equation and interface boundary condition, and on the other hand, it is the process of solving the boundary value definite solution problem.In a word, the solution to the scattering on the boundary surface of seismic wave is to determine the boundary value solution problem satisfied by the wave equation, and then to find out the solution function of the boundary value definite solution problem.However, the boundary value determination problem is divided into displacement potential and displacement expression, so there are two different research methods.The displacement potential function is used to study, which is called "displacement potential method", and the typical representation of displacement potential method is "Knott" equation.The method of displacement function is called displacement method, and the typical representative of displacement method is Zoeppritz equation.The displacement method and the displacement potential method are consistent in physical meaning, but there are some differences in the mathematical solution.This paper mainly deals with the equations of displacement potential amplitude when plane longitudinal wave harmonics are emitted onto the elastic medium boundary surface to produce reflected P-wave, reflected S-wave, transmitted P-wave and transmitted S-wave.In this paper, the displacement-wave function is used to discuss some basic problems about the Zoeppritz equation, mainly including the boundary value solution problem in the form of displacement and the solution function for the boundary value definite solution problem.The Zoeppritz equations of P-wave and SV wave incident from four quadrants in seismic exploration coordinate system are deduced.To solve the Zoeppritz equation, a plane wave function satisfying the wave equation of definite solution is first set up. The wave function consists of five concrete waves: incident wave, reflection wave of the same type, transmission wave of the same type, and converted reflection wave and converted transmission wave.The polarization direction of the volume element on these wave rays is defined, and then the wave function is substituted into the interface equation. At the same time, we also define the reflection coefficient and the transmission coefficient. The final solution function is the corresponding Zoeppritz equation.Then the Zoeppritz equation is numerically calculated and the scattering law of seismic waves on the interface of different conditions can be more clearly and thoroughly understood by numerical calculation.When the angle of incidence reaches the critical angle, the transmitted wave glides along the interface, and when the angle of incidence is greater than the critical angle, the transmitted wave degenerates into an inhomogeneous wave, and the wave number and reflection coefficient of the inhomogeneous wave are both complex.The wide angle reflection receives this energy.We find that the amplitude and phase change rapidly near the critical angle by synthetic seismogram, and the coaxial distortion of reflection wave is complicated by the existence of critical angle.
【学位授予单位】：西南石油大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：P631.4

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